The figure, not drawn to scale, shows a rectangle, ABCD, which is divided in 4 parts, E, F, G, and H. The ratio of the area of H to the area of G is 1 : 2. The ratio of the area of G to the area of F is 9 : 10. If the area of E is 132 cm
2, what is the area of the rectangle ABCD?
H |
G |
F |
E |
1x9 |
2x9 |
|
|
|
9x2 |
10x2 |
|
9 u |
18 u |
20 u |
11 u |
Area G is the repeated identity.
LCM of 2 and 9 = 18
Half of the area of the rectangle
= Area H + Area F
= 9 u + 20 u
= 29 u
Area of E
= Half of the area of the rectangle - Area G
= 29 u - 18 u
= 11 u
11 u = 132
1 u = 132 ÷ 11 = 12
Area of the rectangle
= 29 u x 2
= 58 u
= 58 x 12
= 696 cm
2 Answer(s): 696 cm
2